Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
17856.2-a1
17856.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
17856.2
\( 2^{6} \cdot 3^{2} \cdot 31 \)
\( 2^{20} \cdot 3^{10} \cdot 31 \)
$1.78914$
$(-2a+1), (6a-5), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$0.724272481$
1.672635649
\( \frac{1160560100}{279} a - \frac{258451496}{93} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -319 a - 67\) , \( 2689 a - 748\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-319a-67\right){x}+2689a-748$
23808.2-a1
23808.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
23808.2
\( 2^{8} \cdot 3 \cdot 31 \)
\( 2^{20} \cdot 3^{4} \cdot 31 \)
$1.92256$
$(-2a+1), (6a-5), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.254476736$
1.448544963
\( \frac{1160560100}{279} a - \frac{258451496}{93} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 107 a + 22\) , \( 183 a - 593\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(107a+22\right){x}+183a-593$
23808.2-b1
23808.2-b
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
23808.2
\( 2^{8} \cdot 3 \cdot 31 \)
\( 2^{20} \cdot 3^{4} \cdot 31 \)
$1.92256$
$(-2a+1), (6a-5), (2)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \)
$1.240179320$
$1.254476736$
3.592911016
\( \frac{1160560100}{279} a - \frac{258451496}{93} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -129 a + 107\) , \( -183 a + 593\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(-129a+107\right){x}-183a+593$
71424.2-f1
71424.2-f
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
71424.2
\( 2^{8} \cdot 3^{2} \cdot 31 \)
\( 2^{20} \cdot 3^{10} \cdot 31 \)
$2.53023$
$(-2a+1), (6a-5), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$0.724272481$
1.672635649
\( \frac{1160560100}{279} a - \frac{258451496}{93} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -66 a + 387\) , \( -3009 a + 681\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-66a+387\right){x}-3009a+681$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.